How to split all triangles from a mesh?
EDIT: Selecting everything in edit mode and pressing Crtl-E then selecting Edge Split will do what you want.

If I understand the question correctly you want each triangle to be separate from the rest of the mesh (so no vertex is used by more than one triangle).

One way to do this is to select everything in edit mode (vertex select is easiest although not necessary), press Alt-E and choose individual faces. Immediately right click to cancel the operation and then press Ctrl-I to select everything but the extruded faces. Once you delete the selected vertices you should be left with a mesh made of individual triangles.